Mathematics of FinanceMCQMTP Oct 22Question 1342 of 512
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A Maruti Zen cost 3,60,000\displaystyle 3,60,000. Its price depreciates at the rate of 10%\displaystyle 10\% p.a. during the first two years and at the rate of 20%\displaystyle 20\% in third year. Also find the total depreciation.

Options

A1,26,720\displaystyle 1,26,720
B1,15,620\displaystyle 1,15,620
C1,25,000\displaystyle 1,25,000
D1,10,520\displaystyle 1,10,520
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Correct Answer

Option a1,26,720\displaystyle 1,26,720

All Options:

  • A1,26,720\displaystyle 1,26,720
  • B1,15,620\displaystyle 1,15,620
  • C1,25,000\displaystyle 1,25,000
  • D1,10,520\displaystyle 1,10,520

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Detailed Solution & Explanation

**Derivation of Total Depreciation** Given: - Initial Cost (V0\displaystyle V_0) = Rs. 3,60,000\displaystyle \text{Rs. }3,60,000 - Depreciation rate for first two years (d1\displaystyle d_1) = 10%\displaystyle 10\% p.a. - Depreciation rate for third year (d2\displaystyle d_2) = 20%\displaystyle 20\% p.a. **Step 1: Calculate the depreciated value after 2 years (V2\displaystyle V_2)** V2=V0(1d1)2V_2 = V_0(1 - d_1)^2 V2=360000(10.10)2V_2 = 360000(1 - 0.10)^2 V2=360000(0.9)2V_2 = 360000(0.9)^2 V2=360000×0.81=Rs. 2,91,600V_2 = 360000 \times 0.81 = \text{Rs. }2,91,600 **Step 2: Calculate the depreciated value after 3 years (V3\displaystyle V_3)** V3=V2(1d2)V_3 = V_2(1 - d_2) V3=291600(10.20)V_3 = 291600(1 - 0.20) V3=291600×0.80=Rs. 2,33,280V_3 = 291600 \times 0.80 = \text{Rs. }2,33,280 **Step 3: Calculate the total depreciation amount** Total Depreciation=V0V3\text{Total Depreciation} = V_0 - V_3 Total Depreciation=360000233280=Rs. 1,26,720\text{Total Depreciation} = 360000 - 233280 = \text{Rs. }1,26,720 Hence, **Option A** is the correct answer.

About This Chapter: Mathematics of Finance

Paper

Paper 3: Quantitative Aptitude

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12-16 Marks

Key Topics

Simple & Compound Interest, Annuity, Perpetuity

The most important mathematical chapter in the entire syllabus. It covers Simple Interest (SI), Compound Interest (CI), Nominal vs Effective rates, Present and Future Value, Annuities (Ordinary and Due), Sinking Funds, and Perpetuities. The concepts learned here are applied heavily in CA Intermediate and Final.

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